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Comparing the Views of the Theory of Objectification and the Onto-Semiotic Approach on the School Algebra Nature and Learning

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Title: Comparing the Views of the Theory of Objectification and the Onto-Semiotic Approach on the School Algebra Nature and Learning
Language: English
Authors: Vergel, Rodolfo (ORCID 0000-0002-0925-3982), Godino, Juan D., Font, Vicenç, Pantano, Óscar L.
Source: Mathematics Education Research Journal. Sep 2023 35(3):475-496.
Availability: Springer. Available from: Springer Nature. One New York Plaza, Suite 4600, New York, NY 10004. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-460-1700; e-mail: customerservice@springernature.com; Web site: https://link.springer.com/
Peer Reviewed: Y
Page Count: 22
Publication Date: 2023
Document Type: Journal Articles
Reports - Evaluative
Descriptors: Algebra, Semiotics, Mathematical Concepts, Theories, Mathematical Logic, Mathematical Models, Mathematics Skills, Thinking Skills
DOI: 10.1007/s13394-021-00400-y
ISSN: 1033-2170
2211-050X
Abstract: The theoretical reflection on the nature of school algebra and the development of algebraic thinking from the first educational levels is a relevant topic in mathematics education. In this paper, we first summarize and clarify the positions held on this topic by two theoretical frameworks: the Theory of Objectification and the Onto-semiotic Approach. We identify concordances and complementarities in the respective conceptions of algebra and of the processes of developing algebraic thinking, as a result of applying these frameworks to analyse some students' responses to a task on numerical patterns. We also analyse and compare the didactic models proposed in both theoretical frameworks for developing algebraic thinking. The analysis of the algebraic thinking and learning episodes is also used to illustrate a general discussion on the identity and boundaries of these theoretical frameworks and the possibilities of coordination and integration.
Abstractor: As Provided
Entry Date: 2023
Accession Number: EJ1390898
Database: ERIC
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  Data: <searchLink fieldCode="AR" term="%22Vergel%2C+Rodolfo%22">Vergel, Rodolfo</searchLink> (ORCID <externalLink term="http://orcid.org/0000-0002-0925-3982">0000-0002-0925-3982</externalLink>)<br /><searchLink fieldCode="AR" term="%22Godino%2C+Juan+D%2E%22">Godino, Juan D.</searchLink><br /><searchLink fieldCode="AR" term="%22Font%2C+Vicenç%22">Font, Vicenç</searchLink><br /><searchLink fieldCode="AR" term="%22Pantano%2C+Óscar+L%2E%22">Pantano, Óscar L.</searchLink>
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  Data: Springer. Available from: Springer Nature. One New York Plaza, Suite 4600, New York, NY 10004. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-460-1700; e-mail: customerservice@springernature.com; Web site: https://link.springer.com/
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  Data: The theoretical reflection on the nature of school algebra and the development of algebraic thinking from the first educational levels is a relevant topic in mathematics education. In this paper, we first summarize and clarify the positions held on this topic by two theoretical frameworks: the Theory of Objectification and the Onto-semiotic Approach. We identify concordances and complementarities in the respective conceptions of algebra and of the processes of developing algebraic thinking, as a result of applying these frameworks to analyse some students' responses to a task on numerical patterns. We also analyse and compare the didactic models proposed in both theoretical frameworks for developing algebraic thinking. The analysis of the algebraic thinking and learning episodes is also used to illustrate a general discussion on the identity and boundaries of these theoretical frameworks and the possibilities of coordination and integration.
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